Jee Mains
If z is a complex number such that $|\mathrm{z}| \geq 1$, then the minimum value of $\left|\mathrm{z}+\frac{1}{2}(3+4 \mathrm{i})\right|$ is
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Solution
According to the question,
$|\mathrm{z}| \geq 1, \mathrm{z}$ lies on or outside the circle whose radius is 1 and centre $(0,0)$
$\left|\mathrm{z}+\frac{1}{2}(3+4 \mathrm{i})\right|=\left|\mathrm{z}-\frac{1}{2}(-3-4 \mathrm{i})\right|=$ distance between z and $\left(-\frac{3}{2},-2\right)$
Min. value of $\left|\mathrm{z}+\frac{3}{2}+2 \mathrm{i}\right|$ is zero
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